Question

The number of points scored by Reuben in the first five basketball games of a season are shown below.

23, 15, 28, 19, 25

What would happen to the data distribution if Reuben scored 23, 30, 15, 22, and 26 points in his next five games?

Group of answer choices

The data distribution would become less peaked and more widely spread.

The data distribution would become less peaked and less widely spread.

The data distribution would become more peaked and more widely spread.

The data distribution would become more peaked and less widely spread.

Answer 1

The correct option is (D).

Explanation:

The data for the number of points scored by Reuben in the first five basketball games of a season are:

A = {23, 15, 28, 19, 25}

And the data for the number of points scored by Reuben in the next five games is:

B = {23, 30, 15, 22, 26}

For the first data there are only 5 observations to draw conclusions about the spread of the data and the peak of the distribution curve.

But after the next five games played by Reuben, there are 10 observations to draw conclusions.

The spread of the data is dependent upon the sample size.

Larger the sample size the smaller is the spread. And hence the distribution curve will be more peaked.

And smaller the sample size the larger is the spread. And hence the distribution curve will be less peaked.

So, after the next five games the distribution of Reuben's score would become more peaked and less widely spread.

The correct option is (D).